The case of Cameron Todd Willingham is the most controversial facing the commission. Willingham was put to death for starting a fire that killed his three young daughters, a blaze critics say was subsequently shown to be accidental.
At Thursday's meeting, the commission discussed a recent opinion by state Attorney General Greg Abbott that said it can only deal with cases that occurred since it was founded in 2005 and with work done by labs accredited by the Texas Department of Public Safety, the (Austin) Texas Tribune reported. Commissioners decided they would use Abbott's opinion as a guideline for new cases.
The commissioners also dismissed an appeal by Sonia Cacy, who was paroled six years into a 99-year sentence for setting fire to her uncle. An arson investigator has since cast doubt on the evidence used against her.
Patricia Willingham-Cox urged the commission to issue a report on her cousin's case. Gov. Rick Perry, who signed Willingham's death warrant, moved to limit the work of the commission after the investigation began.
"You can't uninvestigate a case you've already investigated. You can't unacknowledge what you've already acknowledged," she said. "Surely, the Willingham case would demand special consideration."
The commission plans to discuss the Willingham case Friday.
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